Stability and Lyapunov functions
Solve the following problem
Consider the system x' = f(x), where f: R^2 into R^2, is defined by:
f(x) = [ (x1)^3 + (x1) (x2)^2 ]
[ (x1)^2 (x2) + (x2)^3 ]
a- Find all equilibrium points of the system.
b- Use an appropriate Lyapunov function to determine the stability of the equilibrium points. If an equilibrium point is stable, is it asymptotically stable ?